A constitutive relation consisting of a differential equationB˙=agr;‖H˙‖ f(H)−B+H˙g(H), whereH˙ is nonzero, and an experimentally determined condition imposed at the points whereH˙ changes sign is shown to provide a remarkably good and useful representation of hysteresis in superconductors. The solutions of the differential equation provide expressions for important hysteresis curves. From analysis based on the ideas of the Bean and Kim models, in which the critical current density is related to the width of the major loop, expressions for the major loop are used to establish a system of nonlinear equations for the critical current density, the equilibrium magnetization, and their derivatives. This system of equations can be used to evaluate free parameters in assumed forms for the critical current density. Here, the equations are used to compute values forJcandMedirectly. Sample calculations with analytic forms off,g, and agr;, and data from measured hysteresis curves are presented.
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